Franziska Hinkelmann

Mathematical modeling is vital to understanding and predicting a biological system. For systems discrete in nature, like many biological systems, algebraic modeling techniques are suitable. Unlike continuous systems, which have a wide range of theorems and software available for model generation (e.g., parameter estimation) and simulation (e.g., solving differential equations), very few tools exist for discrete networks. My research goal is to find practical methods to analyze the dynamics of discrete models using abstract algebra in place of complex computations.

An agent-based simulation of a complex system consists of agents and rules that describe how they interact. They are especially suitable for systems with a spatial component. A well known example of an agent-based simulation is the model for the spread of an infectious disease by social interaction among agents (humans). My current research focuses on developing an algorithm to approximate an agent-based model with an algebraic model in which I can formalize optimal control theory.

My collaborators and I are working with polynomial dynamical systems (PDS) as discrete models for biological systems. Using PDS we are able to leverage developed theorems from abstract algebra and computer algebra systems for efficient computations. One of our current projects combines algebraic algorithms to generate a model from input data and determine its dynamics through a web interface easily accessible by life scientists (Parameter estimation for Boolean models of biological networks ).